Servo Motors!
It'll probably be worth less in the end to convert it to a VintageAir setup, and work from that.

Is there a chance that some models of your car (Don't know what you have) come with an upgraded HVAC system (maybe with A/C)? With my car, the base model has two sliders and some vacuum tubes I think. My model came with A/C and it uses only wires.

Otherwise, if you still really want to do it, you'll probably want to use stepper motors or servos to control the system. If you work in the automation field and you're adept at building robots, then this will be a piece of cake.